#Centroid equation systems how to#
#Centroid equation systems driver#
#Centroid equation systems full#

Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible bodyвЂ™s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems.

#Centroid equation systems how to#

How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering.

#Centroid equation systems full#

In contrast with the full-rotation approach, arc-based smoothing remains usable when the geometry precludes wobbling the beams around a full circle, e.g., for the X-target and some classes of distributed-radiator targets.Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It is found that, for small numbers of beams on the ring, the arc-based smoothing approach offers superior uniformity. In particular, we assess the potential of these approaches for minimization of azimuthal asymmetry, for the case of a ring of beams arranged on a cone. Here, we describe the arc-based smoothing approach and compare it to results obtainable using an elliptical-beam prescription. This work builds on two earlier concepts: elliptical beams applied to a distributed-radiator target and beams that are wobbled so as to trace a number of full rotations around a circular or elliptical path. In this technique, uniformity is achieved in the time-averaged sense moreВ В» this is sufficient provided the beam oscillation timescale is short relative to the hydrodynamic timescale of the target implosion. Here, we consider an approach to such smoothing that is based on rapidly 'wobbling' each of the beams back and forth along a short arc-shaped path, via oscillating fields applied upstream of the final pulse compression. A uniform energy deposition pattern is important for applications including ion-beam-driven high energy density physics and heavy-ion beam-driven inertial fusion energy ('heavy-ion fusion').

= ,Д«y manipulating a set of ion beams upstream of a target, it is possible to arrange for a smoother deposition pattern, so as to achieve more uniform illumination of the target.

#Centroid equation systems driver#

A conceptual design of the wobbler system for a heavy ion fusion driver is briefly summarized. This is a preferred situation for the beam wobbling technique, because moreВ В» the wobbler system can be designed to generate the desired centroid motion on the target without considering its effects on the envelope and emittance. If the conducting wall is far away from the beam, then the envelope dynamics and centroid dynamics are completely decoupled. Using a model based on moments of the Vlasov-Maxwell equations, we show that the wobbler deflection force acts only on the centroid motion, and that the envelope dynamics are independent of the wobbler fields. The centroid dynamics is controlled by a set of biased electrical plates called 'wobblers'. The basic idea of this technique is to induce an oscillatory motion of the centroid for each transverse slice of the beam in such a way that the centroids of different slices strike different locations on the target. The dynamics of the beam centroid can be explored as a possible beam smoothing technique to achieve a uniform illumination over a suitably chosen region of the target. To realize these advanced, high-gain schemes based on direct drive, it is necessary to develop a reliable beam smoothing technique to mitigate instabilities and facilitate uniform deposition on the target. Recent heavy ion fusion target studies show that it is possible to achieve ignition with direct drive and energy gain larger than 100 at 1MJ.